The generative approach requires much more thought to apply in practice since there are a large number of ways we can decompose the joint distribution into a product of factors. Since each possible decomposition implicitly encodes a particular number of modeling assumptions, the researcher is forced to examine the validity of and the motivation for all modeling assumptions. Furthermore, each component of the factorization needs to be assigned a probability distribution that respects the plausibility of what is known about the putative mechanism that gives rise to the data. For instance, in order to treat the measurements as random in the first place, we would need to first quantify the sources of uncertainty in inherent in the randomness using a statistical model. Randomness can arise from either experimental error, model inadequacy, parametric variability induced by random sampling from a population, or even parameter uncertainty arising from our inability to exactly know the true values of the parameters [1]}.
